Theorem exp45

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

	Ref	Expression
Hypothesis	exp45.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) → 𝜏 )
Assertion	exp45	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp45.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) → 𝜏 )
2	1	exp32	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) )
3	2	exp4a	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )